Answer: 6.6 10 22 atooms
Explanation: You know that the mass of an individual lead atom is equal to
3.4
⋅
10
−
22
grams.
A substance's density tells you what its mass per unit of volume is. In this case, you know that lead has a density of
11.3 g/cm
3
, which means that each
cm
3
of lead will have a mass of
11.3 g
.
Now, your cube has a volume of
2.00 cm
3
, which means that its mass will be equal to
2.00
cm
3
⋅
density
11.3 g
1
cm
3
=
22.6 g
Now all you have to do is look at the mass of one lead atom and figure out exactly how many lead atoms would be needed to make the total mass of the cube equal to
22.6 g
.
22.6
g
⋅
the mass per atom
1 lead atom
3.4
⋅
10
−
22
g
=
6.647
⋅
10
22
lead atoms
Rounded to two sig figs, the number of sig figs you have for the mass of an individual lead atom, the answer will be
no. of lead atoms
=
6.6
⋅
10
22
atoms
You can double-check this result by using lead's molar mass, which tells you what the exact mass of one mole of lead is.
22.6
g
⋅
1 mole Pb
207.2
g
=
0.1091 moles Pb
Now use Avogadro's number to determine how many atoms of lead you have in that many moles
0.1091
moles
⋅
6.022
⋅
10
23
atoms
1
mole
=
6.57
⋅
10
22
atoms
To two sig figs, you will once again get
no. of lead atoms
=